Identifier
-
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St000372: Permutations ⟶ ℤ
Values
[1] => [.,.] => [1] => 0
[1,2] => [.,[.,.]] => [2,1] => 0
[2,1] => [[.,.],.] => [1,2] => 0
[1,2,3] => [.,[.,[.,.]]] => [3,2,1] => 0
[1,3,2] => [.,[[.,.],.]] => [2,3,1] => 0
[2,1,3] => [[.,.],[.,.]] => [3,1,2] => 0
[2,3,1] => [[.,.],[.,.]] => [3,1,2] => 0
[3,1,2] => [[.,[.,.]],.] => [2,1,3] => 0
[3,2,1] => [[[.,.],.],.] => [1,2,3] => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[1,2,4,3] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 0
[1,3,2,4] => [.,[[.,.],[.,.]]] => [4,2,3,1] => 0
[1,3,4,2] => [.,[[.,.],[.,.]]] => [4,2,3,1] => 0
[1,4,2,3] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 0
[1,4,3,2] => [.,[[[.,.],.],.]] => [2,3,4,1] => 1
[2,1,3,4] => [[.,.],[.,[.,.]]] => [4,3,1,2] => 0
[2,1,4,3] => [[.,.],[[.,.],.]] => [3,4,1,2] => 0
[2,3,1,4] => [[.,.],[.,[.,.]]] => [4,3,1,2] => 0
[2,3,4,1] => [[.,.],[.,[.,.]]] => [4,3,1,2] => 0
[2,4,1,3] => [[.,.],[[.,.],.]] => [3,4,1,2] => 0
[2,4,3,1] => [[.,.],[[.,.],.]] => [3,4,1,2] => 0
[3,1,2,4] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 0
[3,1,4,2] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 0
[3,2,1,4] => [[[.,.],.],[.,.]] => [4,1,2,3] => 1
[3,2,4,1] => [[[.,.],.],[.,.]] => [4,1,2,3] => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 0
[3,4,2,1] => [[[.,.],.],[.,.]] => [4,1,2,3] => 1
[4,1,2,3] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 0
[4,1,3,2] => [[.,[[.,.],.]],.] => [2,3,1,4] => 1
[4,2,1,3] => [[[.,.],[.,.]],.] => [3,1,2,4] => 1
[4,2,3,1] => [[[.,.],[.,.]],.] => [3,1,2,4] => 1
[4,3,1,2] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[4,3,2,1] => [[[[.,.],.],.],.] => [1,2,3,4] => 2
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 0
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 0
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 0
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 0
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 0
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 1
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 1
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 0
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 1
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1
[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 1
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 1
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 2
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 1
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0
[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 0
[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0
[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 0
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0
[2,5,1,4,3] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 1
[2,5,3,1,4] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0
[2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 0
[2,5,4,1,3] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 1
[2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 1
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 0
[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 1
[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
>>> Load all 874 entries. <<<[3,5,2,1,4] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[3,5,2,4,1] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[3,5,4,1,2] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 0
[3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 1
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 0
[4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 0
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 1
[4,1,3,5,2] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 1
[4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 0
[4,1,5,3,2] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 1
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,2,1,5,3] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,2,5,3,1] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1
[4,3,1,5,2] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 2
[4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 2
[4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1
[4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 2
[4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 0
[4,5,1,3,2] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 1
[4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 1
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1
[4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 2
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 0
[5,1,2,4,3] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1
[5,1,3,2,4] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 1
[5,1,3,4,2] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 1
[5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1
[5,1,4,3,2] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 2
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 1
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 2
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 1
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 1
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 2
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 2
[5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1
[5,3,1,4,2] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1
[5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 2
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 2
[5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1
[5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 2
[5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1
[5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 2
[5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 2
[5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 2
[5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 2
[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 3
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 0
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 0
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 0
[1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 0
[1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 0
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 1
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 0
[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 0
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 0
[1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 0
[1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 0
[1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 0
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 0
[1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 0
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 1
[1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 1
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 0
[1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 1
[1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 0
[1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 1
[1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 1
[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 1
[1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 1
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 2
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 0
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 0
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 0
[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 1
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 0
[1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 0
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 0
[1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 0
[1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 0
[1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 0
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 0
[1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 0
[1,3,6,2,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 1
[1,3,6,4,2,5] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 0
[1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 0
[1,3,6,5,2,4] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 1
[1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 1
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,2,6,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,3,6,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 0
[1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,6,3,2,5] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,4,6,3,5,2] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,4,6,5,2,3] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 0
[1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 0
[1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 0
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 1
[1,5,2,4,6,3] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 1
[1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 0
[1,5,2,6,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 1
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,3,2,6,4] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,3,6,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 1
[1,5,4,2,6,3] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 1
[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 2
[1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 2
[1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 1
[1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 2
[1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 0
[1,5,6,2,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 1
[1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,6,3,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 1
[1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 2
[1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 0
[1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 1
[1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 1
[1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 1
[1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 1
[1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 2
[1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 1
[1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 2
[1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 1
[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 1
[1,6,3,5,2,4] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 2
[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 2
[1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 1
[1,6,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 1
[1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 2
[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 2
[1,6,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 1
[1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 2
[1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 1
[1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 2
[1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 2
[1,6,5,3,4,2] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 2
[1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 2
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 3
[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 0
[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 0
[2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 0
[2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 1
[2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 0
[2,1,6,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 1
[2,1,6,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,1,6,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 1
[2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 0
[2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 0
[2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 0
[2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 1
[2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 0
[2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 0
[2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 0
[2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 0
[2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 0
[2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 0
[2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 0
[2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 0
[2,3,6,1,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 1
[2,3,6,4,1,5] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 0
[2,3,6,4,5,1] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 0
[2,3,6,5,1,4] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 1
[2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 1
[2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,1,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,3,6,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 0
[2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,6,1,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,6,3,1,5] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,6,3,5,1] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,6,5,1,3] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,1,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,1,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,1,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,3,1,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,3,1,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,3,6,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,4,1,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,4,1,6,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,4,6,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,6,1,4,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,6,3,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 0
[2,5,6,4,1,3] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 1
[2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 0
[2,6,1,3,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 1
[2,6,1,4,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,1,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,1,5,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 1
[2,6,1,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[2,6,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 0
[2,6,3,1,5,4] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 1
[2,6,3,4,1,5] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 0
[2,6,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 0
[2,6,3,5,1,4] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 1
[2,6,3,5,4,1] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 1
[2,6,4,1,3,5] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,4,1,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,4,3,1,5] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,4,3,5,1] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,4,5,1,3] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,4,5,3,1] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 1
[2,6,5,1,3,4] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 1
[2,6,5,1,4,3] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[2,6,5,3,1,4] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 1
[2,6,5,3,4,1] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 1
[2,6,5,4,1,3] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,1,2,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,1,4,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,5,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,5,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,5,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,1,6,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,1,6,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,1,6,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,1,6,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,1,6,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,5,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,5,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,2,6,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,2,6,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,2,6,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,2,6,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,1,6,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 0
[3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 1
[3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,6,1,5,2] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,6,2,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,4,6,2,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,4,6,5,1,2] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 0
[3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 1
[3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,1,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,1,6,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,2,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,2,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,2,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,2,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,2,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,2,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,4,1,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,4,1,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,4,6,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,6,1,4,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,6,2,1,4] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,6,2,4,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,5,6,4,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 0
[3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 1
[3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,1,2,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,1,4,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,1,5,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,2,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,2,1,5,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,6,2,4,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,2,4,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,2,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,6,2,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,6,4,1,2,5] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,4,1,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,4,2,1,5] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,4,2,5,1] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,4,5,1,2] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 0
[3,6,4,5,2,1] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 1
[3,6,5,1,2,4] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,5,1,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,5,2,1,4] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,6,5,2,4,1] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[3,6,5,4,1,2] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 2
[4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,2,6,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,3,2,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,1,3,5,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,3,5,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,3,6,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,1,3,6,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,5,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,5,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,1,5,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,6,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,6,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,1,6,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,1,6,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,1,6,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,1,3,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,1,5,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,1,5,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,1,6,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,1,6,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,3,6,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,3,6,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,5,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,5,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,5,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,5,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,5,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,6,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,6,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,6,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,2,6,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,1,2,6,5] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,1,5,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,1,5,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,1,6,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,2,6,1,5] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,5,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,3,6,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,6,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,6,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,3,6,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,3,6,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,5,1,3,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,5,1,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,5,1,6,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,2,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,2,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,2,6,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,5,3,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 0
[4,5,6,1,3,2] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 1
[4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 1
[4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 2
[4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,6,1,2,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,6,1,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,6,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,6,1,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,6,2,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,2,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,2,3,1,5] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,2,3,5,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,2,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,2,5,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,3,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,6,3,2,1,5] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,6,3,2,5,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,6,3,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,6,3,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[4,6,5,1,2,3] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 0
[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 1
[4,6,5,2,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,5,2,3,1] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 1
[4,6,5,3,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 2
[5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 0
[5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 0
[5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[5,1,2,4,6,3] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 0
[5,1,2,6,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[5,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,3,2,6,4] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,3,4,6,2] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,3,6,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[5,1,4,2,6,3] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[5,1,4,3,6,2] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[5,1,4,6,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[5,1,4,6,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 0
[5,1,6,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[5,1,6,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,6,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,1,6,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[5,1,6,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,1,3,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,1,4,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,1,4,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,1,6,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,1,6,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,3,1,6,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,3,6,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,4,1,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,4,1,6,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,4,3,6,1] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,4,6,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,4,6,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,6,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,6,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,6,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,2,6,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,1,6,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,2,1,6,4] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,2,6,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,6,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,6,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,3,6,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 1
[5,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 1
[5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 2
[5,4,1,3,6,2] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 2
[5,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 1
[5,4,1,6,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 2
[5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,2,1,6,3] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,2,6,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,2,6,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 2
[5,4,3,1,6,2] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 2
[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 3
[5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 3
[5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 2
[5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 3
[5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 1
[5,4,6,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 2
[5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 2
[5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 3
[5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 0
[5,6,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[5,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 1
[5,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[5,6,1,4,3,2] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,6,2,1,4,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 1
[5,6,2,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,6,2,4,3,1] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 2
[5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,6,3,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 2
[5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 1
[5,6,4,1,3,2] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 2
[5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 2
[5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 2
[5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 3
[6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 0
[6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 1
[6,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 1
[6,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 1
[6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 1
[6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 2
[6,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 1
[6,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 2
[6,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 1
[6,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 1
[6,1,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 2
[6,1,3,5,4,2] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 2
[6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 1
[6,1,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 1
[6,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 2
[6,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 2
[6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 1
[6,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 2
[6,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 1
[6,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 2
[6,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 2
[6,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 2
[6,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 2
[6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 3
[6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 1
[6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 2
[6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 2
[6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 3
[6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 1
[6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 2
[6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 1
[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 1
[6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 2
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 2
[6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 2
[6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 2
[6,2,5,1,4,3] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 3
[6,2,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 2
[6,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 2
[6,2,5,4,1,3] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 3
[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 3
[6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,1,4,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,1,4,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 1
[6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 2
[6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 2
[6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 3
[6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 1
[6,4,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 1
[6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 2
[6,4,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 2
[6,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 1
[6,4,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 2
[6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 2
[6,4,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 2
[6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 3
[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 3
[6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 2
[6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 3
[6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 1
[6,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 2
[6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 2
[6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 2
[6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 3
[6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 1
[6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 2
[6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 2
[6,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 2
[6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 2
[6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 3
[6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 2
[6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 3
[6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 2
[6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 2
[6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 3
[6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 3
[6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 2
[6,5,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 2
[6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 3
[6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 3
[6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 2
[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 3
[6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 2
[6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 3
[6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 3
[6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 3
[6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 3
[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 4
[7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 5
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
5,1 15,8,1 52,51,16,1 203,312,172,32,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 5 + q$
$F_{4} = 15 + 8\ q + q^{2}$
$F_{5} = 52 + 51\ q + 16\ q^{2} + q^{3}$
$F_{6} = 203 + 312\ q + 172\ q^{2} + 32\ q^{3} + q^{4}$
Description
The number of mid points of increasing subsequences of length 3 in a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the number of indices $j$ such that there exist indices $i,k$ with $i < j < k$ and $\pi(i) < \pi(j) < \pi(k)$.
The generating function is given by [1].
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the number of indices $j$ such that there exist indices $i,k$ with $i < j < k$ and $\pi(i) < \pi(j) < \pi(k)$.
The generating function is given by [1].
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!